Patent Application
20180173527
The present disclosure relates to a processor and, more specifically, to an instruction set architecture (ISA) associated with the processor, where each of the floating point instructions of the ISA specifies the rounding rule specifically applicable to that floating point instruction.
Processors (e.g., central processing units (CPUs)) may execute software applications including system software (e.g., the operating system) and user software applications. The microarchitecture of a processor may be designed according to an instruction set architecture (ISA) that specifies a set of instructions. A software program can be compiled into a collection of these instructions that can be executed on an execution pipeline of the processor. The instructions specified in the ISA may include instructions processing floating point values (e.g., as inputs or as outputs). These instructions are referred to as floating point instructions of the ISA.
The disclosure will be understood more fully from the detailed description given below and from the accompanying drawings of various embodiments of the disclosure. The drawings, however, should not be taken to limit the disclosure to the specific embodiments, but are for explanation and understanding only.
In a computer, floating point values may be represented using a number of bits that can be interpreted as a representation of a real number. One common representation is the binary32 format as defined according to the IEEE 754 technical standard. The 32 bits of the binary32 format may include a sign bit (S), 8 exponent bits, and 23 fraction bits.
A 32-bit word encoded in this format can be converted into a real number using the following pseudo code as shown in Table 1:
In this example, the sign bit S is used to determine whether the real number is a positive (+) number or a negative (−) number, where the exponent value 255 (i.e. all 1s) is used to represent +/− Infinity and other exceptional conditions. A representation that uses a finite number of bits can only represent a finite number of real values; in particular, there are some real numbers that cannot be represented using the representation. For example, the IEEE binary32 format can represent at most 232 real values. This means that certain real numbers cannot be represented.
Consider the decimal numbers 33554432 (in hexadecimal, 0x200_0000) and the number 1. Both of these two numbers can be exactly represented, in the binary32 format, as S=0, Exponent=152, Fraction=0 and S=0, Exponent=127, Fraction=0 respectively. Their sum 33554433 (0x200_0001), however, cannot be represented in this format because the representation of the sum requires a 25-bit fraction which exceeds the number of bits assigned to the fraction portion of the binary32 format.
When a real value cannot be exactly represented in a particular floating point format, a rounding operation may occur. In some implementations, the rounding operation is to choose an alternative real number that can be represented in that format (e.g., the binary32 format). Typically, the chosen alternative real number can be either the next largest representable real number or the next smallest representable real number.
When performing floating point operations such as addition, subtraction, multiplication, and/or division, frequently the exact result of these operations cannot be represented in the floating point format. In this situation, a processor may need to execute a rounding operation to determine an alternative number that can be represented. The processor may choose a particular rounding method based on the rounding rules. Some of the rounding rules that can be used are:
The application of different rounding rules can produce different rounding results.
The rounding may also occur in a processor when a floating-point number is converted into an integer number. In that case, the processor may convert the real value represented by the floating-point format to the closest integer using a determined rounding rule. The integer results can differ depending on the rounding rule used. For example, consider the following examples as shown in Table 2. Using different rounding rules may produce different results.
Rounding can also arise in the case of integer to floating point conversion. For example, when converting a 32 bit integer represented in an integer format to a binary32 bit format, the integer number 0x200_0001 is not exactly representable, and is rounded, possibly to 0x200_0000 or to 0x200_0004 before conversion.
In some implementations of a processor, the rounding rule is determined in the specification of the processor architecture. In other implementations, the rounding rules that can be used are specified in a register (referred to as a floating-point control register) accessible by the processor through a programming interface. In this scenario, when a floating point operation (or a floating point/integer conversion) generates a non-representable result, the processor examines the floating-point control register to determine which the rounding rule to apply, and the result is rounded based on that the determined rounding rule.
The choice of the rounding rule being used can affect the overall result of a sequence of floating point operations. Consequently, in specialized applications, picking different rounding rules can result in a higher or lower quality final result. In such applications, the program may select an appropriate rounding rule (or rules). However, commonly, a software application does not specify the rounding rule used in a floating point operations. When the rule is not specified, a default rounding rule is used. The default rounding rule is generally associated with a programming language, and is often the round-to-nearest rule.
The choice of rounding method when converting from a floating-point number to an integer can be explicitly defined as rounding functions in a function library of the programming language. A programmer can then use these rounding functions (e.g., ceiling, round, or floor) in code to explicitly apply the desired rounding rule to a particular number.
In the case where the only way to control the floating point rounding mode is the floating point control register, a library function that explicitly specifies the rounding mode would increase the overhead related to managing the rounding mode. For example, the pseudo-code sequence for the ceiling function is shown in Table 3.
where it is noted that of three out of the five lines of instructions in this code sequence are related to manipulating the rounding mode, which causes an increase of the computation overhead.
Frequently switching the rounding mode can be computationally expensive, particularly in the context of modern out-of-order superscalar processors. In some implementations, reading and/or writing the rounding mode can consume a multiple processor cycles. It is often a serializing operation, inhibiting parallel and out-of-order floating point execution.
There are cases that arise where, in a sequence of code, the rounding mode needs to be changed frequently. One example is in a C program where generally, floating point operations are performed with round-to-nearest, while floating-point to integer conversions are specified using round-to-zero. This means a sequence of operations that involves floating point operations that are then rounded to integers would have frequent rounding mode changes. Another scenario that arises is where a user explicitly desires to control the floating-point rounding mode being applied to a particular region of the code. To properly support this functionality, the floating-point rounding mode register needs to be reset to the default mode for the language every time control leaves that region of code. This turns out to be quite expensive as well.
Embodiments of the present disclosure provide for an instruction set architecture including instructions that specify the rounding rule to be applied to a floating-point instruction that may require rounding. In one embodiment, the instruction can directly specify a rounding rule as an attribute of the instruction. If a particular rounding mode is required by a language, the rounding rule can be explicitly encoded using an immediate value in the instruction, thus avoiding the need to manage a floating-point register. In another embodiment, the instruction may specify that the identifier representing a rounding-rule for the instruction be read from a floating-point control register. This supports the case where the user wishes to exert control over the rounding rule used, and dynamically change the rounding rule in an application program. Thus, embodiments of the present disclosure provide means for a floating point instruction, including floating point conversion instructions, of an ISA to exactly specify the desired rounding-mode, or to specify that a default rounding mode provided by a floating-point control register be used.
Processor 102 may include a register file 106 which may further include registers 108, 109 associated with processor 102. In one embodiment, register file 106 may include general purpose registers 108, 109 that each may include a certain number (referred to as the “length”) of bits to store data items processed by instructions executed in pipeline 104. For example, depending on implementations, registers 108, 109 can be 64-bit, 128-bit, 256-bit, or 512-bit registers. Each of the registers 108, 109 may store one or more data items. Registers 108, 109 may be implemented to store floating-point data items and/or fixed-point data items, where the floating-point data items may represent real numbers and the fixed-point data items may represent integers.
The source code of a program may be compiled into a series of machine-executable instructions defined in an instruction set architecture (ISA) associated with processor 102. When processor 102 starts to execute the executable instructions, these machine-executable instructions may be placed on pipeline 104 to be executed sequentially. Instruction fetch/decode stage 110 may retrieve an instruction placed on pipeline 104 and identify an identifier associated with the instruction. The instruction identifier may associate the received instruction with a circuit implementation of the instruction 118 specified in the ISA of processor 102.
The instructions specified in the ISA may be designed to process data items stored in general purpose registers (GPRs) 108, 109. Data fetch stage 112 may retrieve data items (e.g., floating-point or fixed-point) to be processed from GPR 108. Execution stage 114 may include logic circuitry to execute instructions specified in the ISA of processor 102.
In one embodiment, the logic circuitry associated with execution stage 114 may include multiple “execution units” (or functional units), each being dedicated to perform one respective instruction. The collection of all instructions performed by these execution units may constitute the instruction set associated with processor 102. After execution of an instruction to process data items retrieved by data fetch stage 112, write back stage 116 may output and store the results in GPRs 108, 109.
In one embodiment, the ISA of processor 102 may define a floating point instruction, and the execution stage 114 of processor 102 may include an execution unit 118 that include hardware implementation of the floating point instruction defined in the ISA. The floating point instruction may include a first field 120 (or operand) to store an identifier of first register 108, a second field 122 (or operand) to store an identifier of second register 109, and a third field 124 (or operand) to store an identifier representing a rounding rule. The instruction, when executed, may include operations to read a first data item (floating-point data item or fixed-point data item), calculate a result value (floating-point data item) based on the first data item stored in the first register, and round the result value using a rounding rule specified in the third field of the instruction to store result in the second register 109. In this way, embodiments of the present disclosure may allow a program to specify a per-instruction rounding rule. The per-instruction rounding rule implementation allows different instructions associated with different rounding rules, rather than employing one rounding rule (e.g., a default rounding rule) for all instructions executed by the processor 102.
In one embodiment, the rounding rule may be identified by an immediate value stored in third field 124. For example, the immediate value can be an integer, and different integer values may correspond to different rounding rules. In another embodiment, third field 124 may store an identifier of a third register 126 of register file 106, where register 126 may store an identifier corresponding to a specific rounding rule. The indirect specification of the rounding rule (e.g., via register 126) may provide further flexibility to a programmer to program an application.
For example, instruction fadd_s_rzero $f3,$f1,$J2 in the GPTX architecture specifies a single precision floating point add of the contents of $f1 with $f2, storing the results back in $f3, using the rounding rule round to zero.
The fixed rounding rules encoded in the FRM value can include:
rnear: round to nearest (e.g., associated with an identifier RNEAR),
rzero: round to zero (e.g., associated with an identifier RZERO),
rdown: round down (e.g., associated with an identifier RDOWN),
rup: round up (e.g., associated with an identifier RUP),
The other encoding available for the FRM identifier is rdyn—which specifies that the rounding rule specified in the floating point control register should be used, thus indirectly specifying the rounding rules (rather than using a fixed rule).
During the conversion from an integer to a floating-point number, the processor may store the integer in a general-purpose register and store the result in a floating-point register. During the copy from the general-purpose register to floating-point register, the integer value is converted to the equivalent floating-point representation, with rounding if necessary. The rounding may similarly occur when the processor executes an instruction that copies a floating point value from the floating point register to a general-purpose registers, where the floating point value is converted to an integer value based on the rounding rule specified in the instruction.
In one implementation of an ISA, these instructions are the fcvtr (floating converted from integer) and rcvtf (integer converting from floating) instructions that the convert an integer stored in a general-purpose register to a floating-point value stored in a floating-point register and a floating-point value in a floating-point register to an integer stored in a general-purpose register, respectively. The FRM field of these instructions may specify the choice of rounding rule to be applied during the conversion.
In the context of instructions that may copy to/from general-purpose registers (e.g., fcvtr or rcvtf), the rounding rules may include an additional rounding rule referred to as the raw rule. In one embodiment, the raw rule may be specified in the rounding rule field 310 of the fcvtr instruction (or field 316 of the rcvtf instruction) with an identifier RAW. Under the raw rule, the bits in the source register (general-purpose or floating-point) are copied directly (e.g., bit-to-bit copy) to the target register (floating-point/general-purpose register) as is, without the conversion. The use of raw rule allows copying of floating point values from a floating-point register to a same (or greater) length general-purpose register and back without disturbing the value.
In the context of instruction that converts a floating-point number to an integer, embodiments of the present disclosure may provide an additional rounding rule relating to the handling of undefined numbers (NaNs). The undefined number may represent an infinity value. This rounding rule may specify the NaNs to integer conversion to be selected to be one of:
In the context of the rcvtf instruction, as shown in
In one embodiment, the ceiling function as shown in Table 3 may be implemented using the rcvtf instruction by the following code of Table 4.
Since the instruction explicitly encodes the rounding rule there is no need to manipulate a floating point control register, thus reducing the overhead associated with switching the rounding modes.
While the disclosure has been described with respect to a limited number of embodiments, those skilled in the art will appreciate numerous modifications and variations there from. It is intended that the appended claims cover all such modifications and variations as fall within the true spirit and scope of this disclosure.
A design may go through various stages, from creation to simulation to fabrication. Data representing a design may represent the design in a number of manners. First, as is useful in simulations, the hardware may be represented using a hardware description language or another functional description language. Additionally, a circuit level model with logic and/or transistor gates may be produced at some stages of the design process. Furthermore, most designs, at some stage, reach a level of data representing the physical placement of various devices in the hardware model. In the case where conventional semiconductor fabrication techniques are used, the data representing the hardware model may be the data specifying the presence or absence of various features on different mask layers for masks used to produce the integrated circuit. In any representation of the design, the data may be stored in any form of a machine readable medium. A memory or a magnetic or optical storage such as a disc may be the machine readable medium to store information transmitted via optical or electrical wave modulated or otherwise generated to transmit such information. When an electrical carrier wave indicating or carrying the code or design is transmitted, to the extent that copying, buffering, or re-transmission of the electrical signal is performed, a new copy is made. Thus, a communication provider or a network provider may store on a tangible, machine-readable medium, at least temporarily, an article, such as information encoded into a carrier wave, embodying techniques of embodiments of the present disclosure.
A module as used herein refers to any combination of hardware, software, and/or firmware. As an example, a module includes hardware, such as a micro-controller, associated with a non-transitory medium to store code adapted to be executed by the micro-controller. Therefore, reference to a module, in one embodiment, refers to the hardware, which is specifically configured to recognize and/or execute the code to be held on a non-transitory medium. Furthermore, in another embodiment, use of a module refers to the non-transitory medium including the code, which is specifically adapted to be executed by the microcontroller to perform predetermined operations. And as can be inferred, in yet another embodiment, the term module (in this example) may refer to the combination of the microcontroller and the non-transitory medium. Often module boundaries that are illustrated as separate commonly vary and potentially overlap. For example, a first and a second module may share hardware, software, firmware, or a combination thereof, while potentially retaining some independent hardware, software, or firmware. In one embodiment, use of the term logic includes hardware, such as transistors, registers, or other hardware, such as programmable logic devices.
Use of the phrase ‘configured to,’ in one embodiment, refers to arranging, putting together, manufacturing, offering to sell, importing and/or designing an apparatus, hardware, logic, or element to perform a designated or determined task. In this example, an apparatus or element thereof that is not operating is still ‘configured to’ perform a designated task if it is designed, coupled, and/or interconnected to perform said designated task. As a purely illustrative example, a logic gate may provide a 0 or a 1 during operation. But a logic gate ‘configured to’ provide an enable signal to a clock does not include every potential logic gate that may provide a 1 or 0. Instead, the logic gate is one coupled in some manner that during operation the 1 or 0 output is to enable the clock. Note once again that use of the term ‘configured to’ does not require operation, but instead focus on the latent state of an apparatus, hardware, and/or element, where in the latent state the apparatus, hardware, and/or element is designed to perform a particular task when the apparatus, hardware, and/or element is operating.
Furthermore, use of the phrases ‘to,’ ‘capable of/to,’ and or ‘operable to,’ in one embodiment, refers to some apparatus, logic, hardware, and/or element designed in such a way to enable use of the apparatus, logic, hardware, and/or element in a specified manner. Note as above that use of to, capable to, or operable to, in one embodiment, refers to the latent state of an apparatus, logic, hardware, and/or element, where the apparatus, logic, hardware, and/or element is not operating but is designed in such a manner to enable use of an apparatus in a specified manner.
A value, as used herein, includes any known representation of a number, a state, a logical state, or a binary logical state. Often, the use of logic levels, logic values, or logical values is also referred to as 1's and 0's, which simply represents binary logic states. For example, a 1 refers to a high logic level and 0 refers to a low logic level. In one embodiment, a storage cell, such as a transistor or flash cell, may be capable of holding a single logical value or multiple logical values. However, other representations of values in computer systems have been used. For example the decimal number ten may also be represented as a binary value of 910 and a hexadecimal letter A. Therefore, a value includes any representation of information capable of being held in a computer system.
Moreover, states may be represented by values or portions of values. As an example, a first value, such as a logical one, may represent a default or initial state, while a second value, such as a logical zero, may represent a non-default state. In addition, the terms reset and set, in one embodiment, refer to a default and an updated value or state, respectively. For example, a default value potentially includes a high logical value, i.e. reset, while an updated value potentially includes a low logical value, i.e. set. Note that any combination of values may be utilized to represent any number of states.
The embodiments of methods, hardware, software, firmware or code set forth above may be implemented via instructions or code stored on a machine-accessible, machine readable, computer accessible, or computer readable medium which are executable by a processing element. A non-transitory machine-accessible/readable medium includes any mechanism that provides (i.e., stores and/or transmits) information in a form readable by a machine, such as a computer or electronic system. For example, a non-transitory machine-accessible medium includes random-access memory (RAM), such as static RAM (SRAM) or dynamic RAM (DRAM); ROM; magnetic or optical storage medium; flash memory devices; electrical storage devices; optical storage devices; acoustical storage devices; other form of storage devices for holding information received from transitory (propagated) signals (e.g., carrier waves, infrared signals, digital signals); etc., which are to be distinguished from the non-transitory mediums that may receive information there from.
Instructions used to program logic to perform embodiments of the disclosure may be stored within a memory in the system, such as DRAM, cache, flash memory, or other storage. Furthermore, the instructions can be distributed via a network or by way of other computer readable media. Thus a machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computer), but is not limited to, floppy diskettes, optical disks, Compact Disc, Read-Only Memory (CD-ROMs), and magneto-optical disks, Read-Only Memory (ROMs), Random Access Memory (RAM), Erasable Programmable Read-Only Memory (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), magnetic or optical cards, flash memory, or a tangible, machine-readable storage used in the transmission of information over the Internet via electrical, optical, acoustical or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.). Accordingly, the computer-readable medium includes any type of tangible machine-readable medium suitable for storing or transmitting electronic instructions or information in a form readable by a machine (e.g., a computer).
Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present disclosure. Thus, the appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.
In the foregoing specification, a detailed description has been given with reference to specific exemplary embodiments. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the disclosure as set forth in the appended claims. The specification and drawings are, accordingly, to be regarded in an illustrative sense rather than a restrictive sense. Furthermore, the foregoing use of embodiment and other exemplarily language does not necessarily refer to the same embodiment or the same example, but may refer to different and distinct embodiments, as well as potentially the same embodiment.
The present application claims priority to U.S. Provisional Application No. 62/434,521 filed on Dec. 15, 2016, the content of which is incorporated by reference herein.
| Number | Date | Country | |
|---|---|---|---|
| 62434521 | Dec 2016 | US |
